The present invention relates to a picture signal processing system in which, in reproducing a shaded picture signal, halftones are reproducing with a small number of a gradation levels. More particularly, the invention relates to a signal processing system in which halftones of high quality are reproduced by minimizing the quantization distortion which is caused by expressing shaded picture signals with few gradation levels by forming averages in quantization steps. In general, in order to record a shaded picture on a recording medium or to display it on a display device, it is necessary for the recording medium itself to have a gradation characteristic.
On the other hand, a method is known in the art in which halftones are expressed on a recording medium which is capable of reproducing only two levels (light and shade levels or binary data). With this method, as is well known in the field of printing, halftones are expressed with the number of dots per unitary area. This is termed dot density modulation.
Recently, facsimile systems have been extensively employed. In these systems, it is desirable to transmit not only letters but also pictures with gradations. In order to meet this requirement, various systems have been proposed in which halftones are recorded on a recording medium which can record only binary data. A typical example of such a method is a dither method. The dither method, because it uses a simple algorithm and is easily realizable, is expected to be applied to a variety of technical fields.
The principle of a conventional dither method will be described with reference to FIG. 1. In FIG. 1, reference character x.sub.ij designates a picture element having a gradation level of n bits/picture elements at coordinates (i, j) in an input picture and c.sub.ij is the threshold of the picture element. The threshold c.sub.ij takes random values representative of a threshold pattern in dither. x.sub.ij and c.sub.ij are compared with a comparator circuit. When x.sub.ij &gt;c.sub.ij, an output picture signal is y.sub.ij =1, and when x.sub.ij .ltoreq.c.sub.ij, the output picture signal is y.sub.ij =0. According to the shading conditions of the input picture, the density of 1's and 0's are varied to express the halftones.
In the case where the gradations of the output picture are expressed with halftones of 2.sup.n levels, c.sub.ij has 2.sup.n thresholds, i.e., takes random values ranging from 0 to 2.sup.n. In this case, one bit of output is provided for one picture element of the input picture. In general, if 2.sup.n dots are outputted as y.sub.k1 (k.times.1=2.sup.n) for n bits/picture-element of an input picture then gradations of 2.sup.n layers can be expressed for each picture element of the input picture, i.e., the gradations for one picture element are expressed with 2.sup.n dots.
In any one of the various conventional systems, halftones are expressed taking advantage of the characteristics of the human eye, specifically the integration effect of the eye. To acceptably represent a picture element of a picture as number of dots per unit area, 16 dots, for example in 4.times.4 arrangement, are required for expressing sixteen gradations, for instance. These dots are averaged by the eye appearing thus as a signal picture element of the proper density. This means that halftones are expressed somewhat at the cost of the resolution of the picture. If, however, the recording medium can be provided with more gradation levels, then the resolution of the picture will be increased as much.
In general, if gradation levels corresponding to six bits, i.e. 64 gradation levels are available, the halftones of a picture can be expressed satisfactorily taking into account the characteristics of the human eye.
If the recording medium can handle gradation levels of 3 bits/picture-element while the input picture signal has gradation levels of 6 bits/picture-element, this is equivalent to making a recording by quantizing 6 bits/picture-element of an input picture-signal into 3 bits/picture-element. This coarse quantization, of course, causes a large quantization distortion. The quantization distortion appears as a false contour, and is most significant in portions of the picture which change abruptly.